"Dry Mode" is most certainly a dehumidification function. To explain this, you need a short lesson in dew point and relative humidity. The warmer air is, the more water it can hold. The cooler it is, the less it can hold. Relative humidity represents how "full" of water the air is at the current temperature. As the air cools, its capacity for water will decrease and relative humidity will go up. When the relative humidity gets close to 100% you have reached the dew point and water will begin to condense out of the air.
This is the effect air conditioning has on room air. During standard cooling operation, the air leaving an AC unit is about 55F. Based on the dew point concept and the air warming back up to room temperature, the relative humidity of a room will be limited to about 50% (room temp of 75F). When an AC unit has a dehumidification option (your "Dry" mode), it will slow down the fan so that the air leaving the unit gets even colder than 55F. This effectively removes more water from the air and maintains a lower relative humidity in the room. For example if the air leaving the coil gets down to 45F, your room humidity will stabilize at approximately 35%.
This is exactly what dehumifiers do, with one exception: they reheat the air before blowing it back into the room. That's why your unit gets colder when you select that option.